Did you redeem the giftcard you purchased before going to iTunes and trying to purchase your songs?
To redeem the card and add the balance to your iTunes account you will need to open the iTunes application on your computer and then select iTunes store to open the store window,
Once it opens can you then click sign on on the top right of the screen and sign into your iTunes account.
Once signed in you should then be able to select redeem in the quick links menu on the right hand column.
When the redemption window opens can you then enter the code under the scratch off panel on the back of the gift card and you shouold then be shon the credit amount in your account.
Once that is done you should then be able to browse to the composer or artist that you wish and then simply click Purchase to buy and download the song to your library.
If you would try that and let me know if you have any issues
When I open the iTunes store, I got the menu with the various types of music, but when I clicked classical, I got a screen with no composers on it. How do I browse the catalog?
The best way to find things in iTunes in my experrience is to use the search box in the top right corner and simply enter the artist's name, Composer or catalog number if you know it.
Other than that you can use the genre to browse but I find it a little clunky and restrictive, however all you do is click the drop down arrow next to the music option in the store.
Let me know if you have any issues